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QUESTION: 1

For the bridge shown Z_{1} = 200 ∠20° Ω, Z_{2} = 150 ∠30° Ω and Z_{3} = 300 ∠-30° Ω. What is the value of Z_{4 }so that the bridge is balanced?

Solution:

At bridge balance condition,

Z_{1} Z_{4 }= Z_{2} Z_{3}

⇒ 200 ∠20° Z_{4} = 150 ∠30° 300 ∠-30°

⇒ Z_{4} = 225 ∠-20° Ω

*Answer can only contain numeric values

QUESTION: 2

A simple slide wire potentiometer is used for measurement of current in the circuit. The voltage drop across a standard resistor of 0.6Ω is balanced at 60 cm. The magnitude of current if the standard cell of 4V is balanced at 50 cm is ______ (in A)

Solution:

Standard cell of 4 V is balanced at 50 cm.

The voltage drop across 60 cm

The working current through the circuit is,

QUESTION: 3

In the bridge circuit shown in figure when then the voltmeter reads

Solution:

At bridge balance condition

(2R) (X_{c}) = (2R) (R)

Given that,

at this condition, bridge is balanced

Hence the voltmeter reading is 0 V.

*Answer can only contain numeric values

QUESTION: 4

A resistance potentiometer has a total resistance of 4 kΩ and is rated 10W. If the range of potentiometer is 0 to 200 mm. then its sensitivity is _______ (in V/mm)

Solution:

R = 4 kΩ

P = 10 W

We know that.

The potentiometer range is 0 to 200 mm.

QUESTION: 5

A length of cable was tested for insulation resistance using loss of charge method. A capacitance formed by sheath of cable of 300 PF is found to have drop in voltage from 300 V to 100 V in 120 seconds. Calculate the insulation resistance of the cable in MΩ

Solution:

Given that = C = 300 pF

V_{1} = 300 V

V_{2} = 100 V

t = 120 S

*Answer can only contain numeric values

QUESTION: 6

Calculate the value of effective resistance (in Ω) at a supply frequency of 100 Hz. (C_{4 }= 2 μF)

Solution:

Under balance condition

Separate and equating real and imaginary part.

*Answer can only contain numeric values

QUESTION: 7

Find the excitation frequency (in Hz) in the Ac Bridge shown in figure under balance condition. The circuit component values are given as

R_{1} = 100 kΩ,

R_{3} = R_{4} = 100 kΩ,

C_{1} = 2 C_{2} = 10 nF

Solution:

under bridge balance condition,

Given that, R_{3} = R_{4}

(1 + jωR_{1}C_{1})(1 + jωR_{2}C_{2}) = jωC_{1}R_{2}

1 + jωR_{1}C_{1 }+ jωR_{2}C_{2 }− ω^{2}R_{1}R_{2}C_{1}C_{2 }= jωC_{1}R_{2}

By comparing real parts on both sides,

By comparing imaginary parts on both sides,

QUESTION: 8

The Schering bridge shown in figure has the following constant R_{1} = 1.5 kΩ, C_{1} = 0.4 μF, R_{2} = 3 kΩ and C_{3} = 0.4 μF at frequency 1 kHz. The dissipation factor is_______

Solution:

Given, R_{1} = 1.5 kΩ

C_{1} = 0.4 μF

R_{2} = 3 kΩ

C_{3} = 0.4 μF

f = 1 kHz

We know that,

and the unknown capacitance

Dissipation factor

= 2πfC_{x}R_{x}

= 2π × 1 × 10^{3} × 0.2 × 10^{-6} × 3 × 10^{3}

= 3.77

*Answer can only contain numeric values

QUESTION: 9

The AC bridge is supplied with a source of frequency 5 kHz as shown in the figure. If the bridge is balanced at R_{1} = 4 R_{2} and C_{3} = 20 μF, the value of unknown capacitor C_{x} is _____ (in μF)

Solution:

At bridge balanced condition,

By comparing imaginary part,

QUESTION: 10

The dc potentiometer shown in the figure has working current of 10 mA with switch S open. Let R_{g} + R_{1} = 100Ω. The galvanometer G can only detect currents greater than 10 μA. The maximum percentage error in the measurement of the unknown e.m.f. E_{x} as calculated from the slider position shown is closest to

Solution:

Given that, when the switch is open.

I_{W} = 10 mA

⇒ R_{x} = 50 Ω.

Length of R_{x} = 5m.

Resistance across 3m = 30 Ω

Resistance across 2m = 20 Ω

Voltage across 20 Ω = 20 × 10 × 10^{-3} = 0.2 V

Errors in the reading are due to R_{g} and R_{1}.

Error = voltage drop across R_{g} and R_{1}

= I_{g} (R_{g} + R_{1})

= 10 × 10^{-6} (100) = 1 mV

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